A well known and simple game to model markets is the glove game where worth is produced by building matching pairs. For glove games, diff erent concepts, like the Shapley value, the restricted Shapley value or the Owen value, yield diff erent distributions of worth. Moreover, computational eff ort of these values is in general very high. This paper provides effi cient allocation formulas of the...

We provide algorithms guaranteeing high levels of privacy by computing uniformly random solutions to stable marriages problems. We also provide efficient algorithms extracting a nonuniformly random solution and guaranteeing t-privacy for any threshold t. The most private solution is expensive and is based on a distributed/shared CSP model of the problem. The most efficient version is based on r...

We show that, in cooperative production games, when the production functions are not concave, the core may well be empty. However, as the number of players increases (subject to some regularity conditions) the relative deficit obtained by using concavified functions decreases to zero. Furthermore, differentiability of the functions will cause the absolute deficit to go to zero. 0. Description o...

We analyze two well-known matching mechanisms—the Gale-Shapley, and the Top Trading Cycles (TTC) mechanisms—in the experimental lab in three different informational settings, and study the role of information in individual decision making. Our results suggest that—in line with the theory—in the college admissions model the Gale-Shapley mechanism outperforms the TTC mechanisms in terms of effici...

This paper investigates three distinctive and intuitive renegotiation bargaining protocols that all yield the Shapley value as the unique subgame perfect equilibrium outcome. These protocols, built on the multi-bidding procedure of Pérez-Castrillo and Wettstein (2001), allow more freedom in multilateral bargaining where rejected players can further negotiate and form coalitions. The self-dualit...

The value of an uncertain outcome (a 'gamble', 'lottery', etc.) to a participant is an evaluation, in the participant's utility scale, of the prospective outcomes: It is an a priori measure of what he expects to obtain (this is the subject of 'utility theory'). In a similar way, one is interested in evaluating a game; that is, measuring the value of each player in the game. Such an approach was...

This paper studies the relation between convexity of TU games and marginal vectors. Shapley (1971) andIchiishi (1981) showed that a game is convex if and only if all marginal vectors are core elements. In Rafels,Ybern (1995) it is shown that if all even marginal vectors are core elements, then all odd marginal vectorsare core elements as well, and vice versa. Hence, if all even or a...

From the famous Gale–Shapley theorem we know that each classical marriage problem admits at least one stable matching. This fact has inspired researchers to search for the maximum number of possible stable matchings, which is equivalent to finding the minimum number of unstable matchings among all such problems of size n. In this paper, we deal with this issue for the Gale–Shapley model with pr...